For the topping: mix oats, flour, brown sugar, ½ cup of white sugar, ½ teaspoon cinnamon, nutmeg, and salt together in a bowl. Combine butter with the flour mixture using fingers or a fork until coarse crumbs form. Stir in walnuts and set aside.
Whisk together ⅓ cup sugar, cornstarch, ginger, and ½ teaspoon cinnamon. Place the apples in a slow cooker, stir in the cornstarch mixture; toss with lemon juice.
Sprinkle the walnut crumb topping on top. Cover and cook on High for 2 hours or Low for 4 hours, until apples are tender.
Partially uncover the slow cooker to allow the topping to harden, and cook for another hour.
Serve with a scoop of vanilla ice cream or top with whipped cream and enjoy!